Pith Number

pith:VSQXPXJH

pith:2018:VSQXPXJHAD4AEMNDQTRBGLH3CL

not attested not anchored not stored refs pending

Large Positive and Negative Values of Hardy's $Z$-Function

Kamalakshya Mahatab

arxiv:1807.08554 v3 · 2018-07-23 · math.NT

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{VSQXPXJHAD4AEMNDQTRBGLH3CL}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Receipt and verification

First computed	2026-05-17T23:59:52.121575Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

aca177dd2700f80231a384e2132cfb12e957677907cf2c670d8ee80bd170592c

Aliases

arxiv: 1807.08554 · arxiv_version: 1807.08554v3 · doi: 10.48550/arxiv.1807.08554 · pith_short_12: VSQXPXJHAD4A · pith_short_16: VSQXPXJHAD4AEMND · pith_short_8: VSQXPXJH

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/VSQXPXJHAD4AEMNDQTRBGLH3CL \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: aca177dd2700f80231a384e2132cfb12e957677907cf2c670d8ee80bd170592c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b7e8667f3f03b8ab49d9cee2addf418cc800ae833654d26f321c02a8009e558e",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2018-07-23T12:12:27Z",
    "title_canon_sha256": "298540da6b36d79272b24f883773827091e28902a731f6e00007c9d30f6d7457"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1807.08554",
    "kind": "arxiv",
    "version": 3
  }
}